Better Than Money

The black market can be found in Sanctuary. You will reach this town pretty early by following the path of the story. From the outside the black market looks like a simple, purple door. It's at the eastern wall of Sanctuary, next to Moxxi's Bar.

To buy items you need Eridium. Eridium can be be gained by completing missions or by killing rare enemies. Sometimes it can also be found in chests. Each basic item / upgrade costs 4 Eridium. You can purchase ammo upgrades, bank slot upgrades, and more.